Lab 2 Modeling from an observed response

Transcription

1 Lab 2 Modeling from an observed response Agenda Time Item 5 min Lab introduction The big picture of system modeling in the time domain 5 min The SEE, to quantify the goodness of fit 5 min Demonstration of collecting step response data for a mass-spring-damper apparatus 145 min Lab activity Modeling of a mass-spring-damper apparatus The big picture: Collect step response data for a mass-springdamper apparatus. Identify the physical parameters for an ideal mass-spring-damper system model from the data. Simulate the model response and compare it to the data graphically and by computing the SEE. Refine the original model to obtain a better fit of model response to data. k m x Compare the refined model response to the data graphically and by computing the SEE to demonstrate improvement. c Write a memo to present and interpret your results. ES 205 Lab 2 Page 1 of 11

2 The big picture of system modeling in the time domain From experiment From applying first principles Run experiment and collect data Draw system schematic, draw KD = FBD, and apply COLM rate to obtain DE model + + = Plot response data Use data to obtain model parameters Simulate and plot response of model Displacement (cm) Time (s) Displacement (cm) Time (s) Compare model to data No Good match between model and data? Improve model fidelity Yes Useable model ES 205 Lab 2 Page 2 of 11

3 The SEE, to quantify the goodness of fit The standard error of estimate (SEE): SEE=,, 2 where is the number of data points. Response (units) Response (units) Time (s) Quantifies the goodness of fit between a model response and data. Standard deviation of data with respect to a model prediction. Has the same units as and. Has little meaning by itself you need to compare it to another computed SEE value. Reminder about computing the SEE: The simulation time array needs to match the data time array tdata. Force Simulink to return the same times in tdata: Be sure to load the data before the running the simulation. In you Matlab script use: >> sim( model,tdata); ES 205 Lab 2 Page 3 of 11

4 Collect the step response data Set up the hardware: 1. If the computer is on, restart it. If the computer is off, turn it on. 2. Turn on the ECP box sitting above the workstation by pressing the black button. 3. Set up the mass-spring-damper system: Fix the middle and right carts. Remove any brass weights from the left cart. Attach a stiff (heavy gauge wire) spring to the cart. If your workstation has an AirPot damper, attach it to the cart. Remove the plug from the back. If not connected, connect the two power/signal cables to the apparatus. Set up the software: 1. Log in to the workstation computer. User name: student Password: student 2. Load the controller personality file for the apparatus. Open the program ECP32: Start > Programs > ECP > ECP32. In ECP32: Utility > Download Controller Personality File. Open m210_rtwt_3.pmc. Close ECP32 when the file is finished loading. 3. Open the files to run the experiment. Open MATLAB R2010a. Change the directory to C:\Documents and Settings\student\Desktop\ES205\Lab34. ES 205 Lab 2 Page 4 of 11

5 Open ECPDSPResetmdl.mdl. Click the Incremental Build button. You may need to make the window wider to find this button. A bunch of stuff will be written to the MATLAB command window, ending with something like ### Successful completion of Real-Time Workshop build procedure for model: ECPDSPResetmdl. Open lab_1_210.mdl. Click the Incremental Build button and wait for the build to complete. Run the experiment: 1. In ECPDSPResetmdl.mdl: Push the Connect to Target button. The Play button should become black. Push the Play button to reset the encoder (which measures the cart position) to zero. 2. In lab_1_210.mdl: Open the Step block. Record the software step amplitude ( final value ): = Calculate the magnitude of the step force applied to the cart: (69.5 N) = N Push the Connect to Target button. The Play button should become black. Push the Play button and watch the cart respond to the supplied step input force. You should see a plot of the measured cart displacement in the figure window that pops up. If the data are distorted in any way, rerun the experiment by repeating Steps 1 and 2. ES 205 Lab 2 Page 5 of 11

6 Call me over if you are having problems running the experiment. 3. Save and transfer the data. The time data is recorded in seconds and stored in the array time. The cart displacement data is recorded in centimeters and stored in the array x1. Save the data using the save command: save filename time x1 (replace filename with the actual file name) Transfer the data file to your laptop using a thumb drive. 4. Shut down the system. Close all programs and shut down the computer. Turn the ECP box off by pressing the red button. ES 205 Lab 2 Page 6 of 11

7 Identify the system parameters from the data Prepare for analysis: Locate your Simulink model and MATLAB m-file from the prelab. Create a copy of these files to use for Lab 2 analysis. Perform all calculations in your m-file. Download and open the Lab 2 memo template from the course website. Do the analysis: 1. Load and plot the step response data (Figure 1 in the Lab 2 memo template). Use the same plotting standards as in previous labs and prelabs (axis labels, markers for data, etc.). 2. Extract the following data from the step response plot and arrays: First peak value: Second peak value: Time to first peak: Time to second peak: Steady-state value: 3. Record,,,, and in Table 1 in the Lab 2 memo template, along with. Use no more than 4 significant digits. Include units. 4. Use the data in Table 1 to calculate the standard form parameters,, and. 5. Record,, and in Table 2 in the Lab 2 memo template, along with (which was calculated). Use no more than 4 significant digits. Include units. 6. Calculate the cart mass, damping coefficient, and spring stiffness from,, and. 7. Record,, and in Table 3 in the Lab 2 memo template. Use no more than 4 significant digits. Include units. ES 205 Lab 2 Page 7 of 11

8 Simulate the model and compare its response to the data Simulate the step response: 1. Use your calculated,, and values to simulate the step response of your mass-spring-damper model. Compare the model response to the data: 2. Plot the model step response and data on the same axes in centimeters (Figure 2 in the Lab 2 memo template). Use the same plotting standards as in previous labs and prelabs (axis labels, legend, markers for data, line for the model response, etc.). 3. Compute the SEE in centimeters to quantify the error in the model prediction. 4. Record the SEE value in Table 3 in the Lab 2 memo template. Use no more than 4 significant digits. Include units. ES 205 Lab 2 Page 8 of 11

9 Refine the model for a better fit of model response to data The model prediction does not quite match the data. The original mass-spring-damper system model is insufficient. Refine the model to better fit the step response data. Remember: the data are true and the model is an estimate. The model requires refinement, not reality. Refining the DE model: Account for Coulomb (dry) friction between the cart and rails: k x m c Modifying the simulation diagram and solver settings: 1. Use the Coulomb & Viscous Friction block: Discontinuities > Coulomb & Viscous Friction ES 205 Lab 2 Page 9 of 11

10 2. You need to change the solver settings in Simulink to solve this refined DE model: In Simulink: Simulation > Model Configuration Parameters > Solver Set Solver to ode15s (stiff/ndf) : Set Algorithm to Adaptive : Update the model: 1. Modify your simulation diagram to incorporate the Coulomb & Viscous Friction block. 2. Modify your m-file to incorporate the Coulomb friction parameters. 3. Run your simulation with =0. Check that you get the same response and SEE value as your original model. If you don t, find the problem and fix it before continuing. Determine refined model parameters: 1. Obtain a lower SEE and a better visual fit between the model and data by Gradually increasing. Making small tweaks to,, and (if necessary). 2. Record your best values for,,,, and the SEE in Table 3 in the Lab 2 memo template. Use no more than 4 significant digits. Include units. 3. Plot the refined model step response and data on the same axes in centimeters (Figure 3 in the Lab 2 memo template). Use the same plotting standards as in previous labs and prelabs (axis labels, legend, markers for data, line for the model response, etc.). ES 205 Lab 2 Page 10 of 11

11 Submit a memo detailing your results As a team, complete the Lab 2 memo: Complete all tables. Include units. Paste in all requested plots. Do NOT use the Snipping Tool. Provide descriptive captions for all tables and figures. For your plot of the original model response and data on the same axes (Figure 2), do the following: 1. Write a paragraph, positioned above the figure, describing what the graph is. What is graphed as a function of what? What is the reader seeing? Refer to the graph by its figure number. 2. Below the figure, write a second paragraph describing what the graph means. How does the model response compare to the data? Use technical language like peak time, settling time, overshoot, steady-state value, etc. What do you infer from comparing the model response to the data? For your plot of the refined model response and data on the same axes (Figure 3), do the following: 1. Write a paragraph, positioned above the figure, describing what the graph is. What is graphed as a function of what? What is the reader seeing? Refer to the graph by its figure number. 2. Below the figure, write a second paragraph describing what the graph means. How does the refined model response compare to the data? Use technical language like peak time, settling time, overshoot, steady-state value, etc. What do you infer from comparing the refined model response to the data? Attach printouts of your final Simulink model and MATLAB m-file (i.e., for the refined model). Submit your Lab 2 memo by the end of the lab period. ES 205 Lab 2 Page 11 of 11